If you want to wish or celebrate a festival you will have to see whether it is within the guidelines of Islam or not??? for example most of festivals of other religions contains shirk. Celebrating or wishing any such festival will be Haram.
This post was specially about wishing Merry Christmas which is a Christian festival celebrated every year on 25th December. If we see the details of Christmas it comes in direct conflict with Islamic Beliefs. When you say Marry Christmas you are actually accepting that Jesus Is begotten son of God Nauzubillah.
So wishing or celebrating Christmas is totally Haram from Islamic point of view. Moreover there is no proof in history that Jesus was born on 25th of December.
We should remember this saying of Rasool Allah SAW that "He does not belong to us who imitates other people."
Jesus Peace Be Upon him was one of the greatest Prophet of God and it is must for every Muslim to believe in him to be a Muslim. But to call him begotten son of God is totally Haram and Shirk.
However We can participate in those festivals of Non-Muslims that not goes against the Islam.